For certain values of $k$ and $m,$ the system a + 2b = -3 - 7a + b, 4a + 2b = k - 5a - mb has infinitely many solutions $(a,b).$ What are $k$ and $m?$
Rearrange as
8a + b = -3 (1)
9a + (2 + m)b = k (2)
This system has infinite solutions when the equations are the same
Multiply (1) by 9 and (2) by 8
72a + 9b = -27
72a + 8(2 + m)b = 8k
So
9 = 8(2+m) -27 = 8k
9 = 16 + 8m k = -27/8
8m = -7
m = -7/8
+1234 
